Problem: $J$ $K$ $L$ If: $ KL = 2x + 5$, $ JK = 5x + 3$, and $ JL = 22$, Find $KL$.
From the diagram, we can see that the total length of ${JL}$ is the sum of ${JK}$ and ${KL}$ $ {JK} + {KL} = {JL}$ Substitute in the expressions that were given for each length: $ {5x + 3} + {2x + 5} = {22}$ Combine like terms: $ 7x + 8 = {22}$ Subtract $8$ from both sides: $ 7x = 14$ Divide both sides by $7$ to find $x$ $ x = 2$ Substitute $2$ for $x$ in the expression that was given for $KL$ $ KL = 2({2}) + 5$ Simplify: $ {KL = 4 + 5}$ Simplify to find ${KL}$ : $ {KL = 9}$